(1) Field of the Invention
This invention relates to a method for providing layouts of a three dimensional workplace and more particularly to a method for determining the physical density or crowding of a three dimensional workplace so as to optimize the layout of the workspace.
(2) Description of the Prior Art
In the inventor's previous patent entitled "Process Which Aids to the Laying Out of Locations of a Limited Number of 100, Personnel and Equipments in Functional Organization", U.S. Pat. No. 5,235,506, which is incorporated into this disclosure in its entirety by reference, a process is described whereby the relationship among objects in a particular two dimensional work area can be accurately determined to minimize crowding. A crowding index, or Population Density Index (PDI), for the work area, termed PDI.sub.act, is calculated and compared to theoretical minimum (PDI.sub.min) and maximum (PDI.sub.max) values, such that PDI.sub.min &lt;PDI.sub.act &lt;PDI.sub.max. The formula for calculating PDI.sub.act is as follows: ##EQU1## where n=number of objects within the work area;
A =the geometric area of the work area; and PA1 d.sub.act =average Euclidean distance among all possible pairs of n objects within the work area. PA1 c=an arbitrary constant which corresponds to the minimum possible spacing between the objects, e.g., personnel standing shoulder to shoulder within a work area would be spaced approximately one foot from head to head, so c would be equal to one foot.
The values of PDI.sub.min and PDI.sub.max are given as follows: ##EQU2## and ##EQU3## where .DELTA.=the average Euclidean distance of all possible pairs of points for a unit lattice, i.e., a lattice of n points uniformly distributed in area A; and
It can be seen that PDI.sub.min corresponds to a uniform distribution of n points within the work area, while PDI.sub.max corresponds to a uniform distribution of n points within the work area with a minimum distance c between each horizontal and vertical point. With these values determined, PDI.sub.act can be optimized to provide the optimum layout for the work area. Two dimensional layouts suffice for a large number of work areas, such as office spaces and typical manufacturing areas. However, for applications where optimum layouts of three dimensional spaces are required, the previous methods are inadequate. Such applications may include space station layouts, robotic manufacturing facilities where robots can operate in any orientation and nano technology structures such as molecular machines. The conventional physical science density measure of the ratio of mass to volume may be used to provide an index of crowding within a three dimensional space. However, this density measure fails to capture the spatial relationship of objects in the space, i.e., moving objects around within the space would not vary the density measure.